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Popular >

expand (y-2)^4

Solution

expand

(y - 2)^{4}

Solution

y^{4} - 8 y^{3} + 24 y^{2} - 32 y + 16

Solution steps

(y - 2)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = y, b = - 2

= i = 0 \sum 4 (i 4) y^{(4 - i)} (- 2)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} y^{4} (- 2)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} y^{3} (- 2)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} y^{2} (- 2)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} y^{1} (- 2)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} y^{0} (- 2)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} y^{4} (- 2)^{0} : y^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} y^{3} (- 2)^{1} : - 8 y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} y^{2} (- 2)^{2} : 24 y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} y^{1} (- 2)^{3} : - 32 y

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} y^{0} (- 2)^{4} : 16

= y^{4} - 8 y^{3} + 24 y^{2} - 32 y + 16

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Frequently Asked Questions (FAQ)

What is expand (y-2)^4 ?
The solution to expand (y-2)^4 is y^4-8y^3+24y^2-32y+16